The use of mechanical resonators as precise sensors for mass, force and other physical parameters has been fueled by recent advances in miniaturization. This is because a lower resonator mass leads to a higher responsivity, i.e. a larger shift of the resonance frequency for a given stimulus [1]}. However, the detection limit of resonant sensors is not only determined by the responsivity, but also by the frequency resolution, which is defined as the smallest resonance frequency change that can be detected. In order to be resolved, a frequency change needs to be larger than the stochastic variations observed when measuring the resonance frequency, which are commonly characterized by the Allan deviation \(\sigma _y\)  [2]}, [3]}. The Allan deviation of a resonant sensor results from the noise sources inherent to the resonator, its environmental conditions, and the noise from the readout [1]}, [5]}, [6]}, [7]}. When all environmental and readout noise sources are eliminated, the fundamental resolution limit at finite temperatures is determined by the resonator's thermomechanical noise. The corresponding Allan deviation, which depends on the integration time of the measurement, has been well established for mechanical resonators in the linear regime [1]}, [9]}.
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